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A143373 Expansion of x / (1-x-2*x^3-2*x^5-x^7). 1

%I

%S 1,1,1,3,5,9,17,30,55,100,181,330,599,1088,1978,3593,6529,11864,21556,

%T 39169,71171,129319,234978,426961,775801,1409655,2561384,4654113,

%U 8456664,15366012,27920509

%N Expansion of x / (1-x-2*x^3-2*x^5-x^7).

%C A new 4 symbol polynomial of the Weaver telegraphic type ( simplified) : dot:x; dash:x^3; Letter space: x^2 ; Word space: x^4 ; p(y)=-1 - 2 y^2 - 2 y^4 - y^6 + y^7.

%C An alternative set of symbols would be:

%C dot:x;

%C dash:x^2;

%C Letter space: x^3 ;

%C Word space: x^4 ;

%D Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37 - 38

%H G. C. Greubel, <a href="/A143373/b143373.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,0,2,0,1).

%e Weaver determinant:

%e Expand[FullSimplify[ExpandAll[y^7 *Det[{{-1, (1/y^3 + 1/y)}, {(1/y^4 + 1/y^2),1/y + 1/y^3 - 1}}]]]].

%t p[y_] = -1 - 2 y^2 - 2 y^4 - y^6 + y^7; q[x_] = ExpandAll[x^13*p[1/x]]; a = Table[SeriesCoefficient[Series[1/q[x], {x, 0, 30}], n], {n, 0, 30}]

%o (PARI) x='x+O('x^50); Vec(x/(1-x-2*x^3-2*x^5-x^7)) \\ _G. C. Greubel_, Sep 27 2017

%Y Cf. A122762.

%K nonn,uned

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 22 2008

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)